I believe the problem is that the current MOT is to be replaced in 2018 by a universal European test which includes criteria (I have no idea what) that some older cars will not be able to meet even if in perfect condition. The obvious answer would seem to be a two-tier test, to ensure that older vehicles meet at least basic safety standards.
I don't really have a problem with the pre-1960 exemption, but a rolling 40 year is going to exempt a lot of high performance cars capable of practical every-day use.